Bishopweed (Aegopodium podagraria 'Variegatum), and Chameleon plant (Houttuynia cordata) are aggressive. If you do a search everybody hates both of these plants because they are aggressive.

I used the bishopweed on a slop at a previous house. It was a slop that lead down to a cement area and I could not climb down to weed or mow.

I have Cotoneaster dammeri on a hillside at my present house but I can get down and weed in that area because it is not as steep as my other house, the dandelions, mustard and some ugly evil prickly weed still grows.

Both the Bishop's weed and houttunyia are herbaceous groundcovers, meaning they die back to the ground in winter, so less than ideal choices both for slope stabilization or for weed control. They DO spread quite aggressively under proper growing conditions, however :-)

I'd really focus on an evergreen groundcover.

Try english ivy!!!

Try crownvetch. You may have to purchase seed not plants.

St. John's Wort! I had no idea how invasive it would be in my perennial border. As I struggled to remove it, I thought, hey, this would be a great groundcover for a difficult slope. And it's semi evergreen.

The reason Crown Vetch is not sold as a plant anymore is because it is highly invasive. It is also deciduous, so the slope will not look attractive in winter. There are superior alternatives out there for erosion control including moss phlox (evergreen) and cotoneasters (some species evergreen).

Here is a link that might be useful: Crown Vetch